System Dynamics of the Open-Draw With Web Adhesion: Particle Approach

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Sverker Edvardsson ◽  
Tetsu Uesaka
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Time Dependent ◽  
Temporal Fluctuation ◽  
Continuous Solutions ◽  
Continuous Growth ◽  
System Parameters ◽  
Paper Machines ◽  
Particle Approach ◽  
The Web

In the present work we propose a particle approach, which is designed to treat complex mechanics and dynamics of the open-draw sections that are still present in many of today’s paper machines. First, known steady-state continuous solutions are successfully reproduced. However, it is shown that since the boundary conditions depend on the solution itself, the solutions for web strain and web path in the open-draw section are generally time-dependent. With a certain set of system parameters, the nonsteady solutions are common. A temporal fluctuation of Young’s modulus, for example, destabilizes the system irreversibly, resulting in the continuous growth of web strain, i.e., break. Finally we exemplify with some strategic draw countermeasures how to prevent a dangerous evolution in the web strain.

The behavior of cambered belts transiting cylindrical rollers

2021 ◽  
pp. 095440892110644
Author(s):  
Jinxin Shi ◽  
Sheng Pan ◽  
Ron E. Markum ◽  
James K. Good
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Length Variation ◽  
Lateral Deformation ◽  
Roll To Roll ◽  
Manufactured Products ◽  
Lateral Behavior ◽  
The Web

The lateral deformations of webs in roll-to-roll process machines can affect the quality of the manufactured products. Webs with simple nonuniform length variation across their width (camber) will steer toward the long side, leading to the steady state lateral deformation and hence registration. Most previous studies have focused on a cambered web in a free span between two rollers. These studies assume some displacement and slope boundary conditions are known and seek the remaining conditions that would dictate the steady state lateral deformation of the web. This article focuses on the lateral behavior of a cambered web belt transiting between two aligned rollers as the simplest case of multiple span cambered web. Dynamic simulation has been conducted to better understand the response of a cambered web under tension that has been witnessed in tests. There are no boundary conditions enforced and no steady state deformation of the cambered webs. Thus there is no closed-form solution to the lateral movement of a cambered web transits over multiple rollers. This explained why the previous research focused more on the experimental exploration without few theoretical validations. The web travels toward the long side continually from one span to the next until a web guide attempts to return the web to an acceptable lateral location in the process machine.

Interaction of Web Spans: Part I—Statics

1989 ◽  
Vol 111 (3) ◽  
pp. 490-496 ◽  
Author(s):  
G. E. Young ◽  
J. J. Shelton ◽  
B. Fang
Keyword(s):  
Boundary Conditions ◽  
Beam Theory ◽  
Edge State ◽  
Proper Choice ◽  
System Parameters ◽  
Tension Distribution ◽  
Static Solutions ◽  
Different Types ◽  
Mode A ◽  
The Web

When the friction between the web and a roller between two web spans is small enough that the tension distribution across the web in the downstream span affects the tension distribution in the upstream span interaction will occur. A model is developed which extends the work of one of the authors to this case and utilizes beam theory which is valid when the web is not in a wrinkled or slack edge state. The boundary conditions and static solutions for the three different types of interaction are established. In the circumferential slippage mode a negative steering effect has been identified. A steering effect description function is established which will allow prediction of this phenomenon which can be avoided by proper choice of system parameters.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

scholarly journals Ground- and excited-state characteristics in photovoltaic polymer N2200

RSC Advances ◽  
2021 ◽  
Author(s):  
Guanzhao Wen ◽  
Xianshao Zou ◽  
Rong Hu ◽  
Jun Peng ◽  
Zhifeng Chen ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Excited State ◽  
Steady State ◽  
Excited States ◽  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Time Dependent ◽  
Functional Theory ◽  
Time Resolved ◽  
Dependent Density

Ground- and excited-states properties of N2200 have been studied by steady-state and time-resolved spectroscopies as well as time-dependent density functional theory calculations.

scholarly journals Geometries with mismatched branes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Andreas Karch ◽  
Lisa Randall
Keyword(s):  
Boundary Conditions ◽  
Effective Action ◽  
Cosmological Models ◽  
Time Dependent ◽  
De Sitter ◽  
Stabilization Mechanism ◽  
New Class ◽  
Vacuum Solutions ◽  
Single Coordinate

Abstract We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

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